Work

From the Optimal $L^2$-Estimates $(p,n)$ and $(n,p)$-Forms to Uniform Griffiths $p$-Positivity via Convolution and Restriction

Year: 2026

Type: preprint

Abstract: We prove that the optimal $L^2$-estimate property for $(p,n)$-forms is preserved under standard convolution regularization. As an application, we show that a singular Hermitian metric satisfying the optimal $L^2$-estimate property for $(p,n)$-forms is uniform Griffiths $p$-positive. By establishing the restriction property, we prove that a singular Hermitian metric satisfying the optimal $L^2$-estimate property for $(n,p)$-forms is also uniform Griffiths $p$-positive.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28236

Authors: Liu, Zhuo, Zhang, Xujun

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223101422

Cites: 7

Cited by:

Related to: 10

From the Optimal $L^2$-Estimates \((p,n)\) and \((n,p)\)-Forms to Uniform Griffiths \(p\)-Positivity via Convolution and Restriction